Dynamical systems are often considered immune from memory effects, i.e., the dependence of their time evolution on the previous history. This assumption has been tested for two phenomena in nuclear fusion that are believed to sometimes show sensitivity to the previous history of the discharge: disruptions and the transition from the L mode to the H mode of confinement. To this end, two neural network architectures, tapped delay lines and recurrent networks of the Elman type, have been applied to the Joint European Torus (JET) database to extract these potential memory effects from the time series of the available signals. Both architectures can detect the dependence on the previous evolution quite effectively. In the case of disruptions, only the ones triggered by locked modes seem to be influenced by the previous history of the discharge. With regard to the L-H transition, memory effects are present only in the time interval very close to the transition, whereas once the plasma has settled down in one of the two regimes, no evidence of dependence on the previous evolution has been detected.